A Logical Graph Game

September 27, 2013

We made a new logic game. In it we drew a graph using circles and lines, and throughout this blog entry when I refer to a graph I’m refering to the type of mathematical graph used in graph theory, representing objects and the links between them, though you don’t need to know anything about graph theory to play the game.

These are the rules: You have to put Xs and Os into the circles and the lines told the relationship between two connected circles. If the line has a heart next to it then the connected circles had the same symbol in it. If the line did not have a heart then the symbols were different. We took turns drawing the graph and solving what goes in each circle. Sometimes we would put a question mark to show that the person solving the puzzle had to decide if it needed a heart or not.

After playing for a while and seeing the patterns (like that three circles joined into a triangle require a heart on one line or three lines) we decided to expand the game. We added another symbol. Now we put Xs, Os, and Stars in. Hearted-lines still meant that the circles had the same symbol, and plain lines still meant having different symbols, but different symbols no longer meant “opposite.” Whereas a square of plain lines could be easily solved if one circle was known before, now it took two circles or an extra line dividing the square into triangles. Most of our maps we did with pen and paper but here is one we made using the computer (with squares instead of circles). Can you solve it?

Making the puzzles are as fun and challenging as solving them! We quickly learned that in order to have each square of the three-symbol puzzle identifiable any square needs to be connected either by a “heart-line” or by two “unhearted lines” touching different identifiable symbols. A square could touch four other squares and still not be identifiable, if those four other squares all contained the same symbol or if their identities were not clear.